Wizualizacje w poznaniu matematycznym a kategoria intuicji przestrzennej
VISUALIZATION IN MATHEMATICS AND SPATIAL INTUITION
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After several decades during which diagrams were neglected as a reliable source of mathematical knowledge, in recent years we have witnessed a revival of interest in the role of diagrams in mathematical cognition. In the paper, I consider how those investigations relate to the concept of spatial intuition and its role in mathematical cognition. It is argued that some characteristics of mathematical cognition that involve the use of diagrams are analogous with characteristics usually attributed to intuitive knowledge, above all the immediacy of access to the analyzed object that intuition is said to deliver. First of all, this is due to the special characteristics of diagrams, such as their structural similarity to the mathematical object represented and their ability to convey a lot of information. However, it is argued that the immediacy of mathematical cognition related to diagrams should not cancel the necessity to use concepts or reasoning, which are in fact indispensable in mathematical practice. Several other possible ways of using the concept of “intuition” are then indicated. One of them is connected with the common distinction between “intuition that” and “intuition of”. Visual “intuition that” is a mathematical belief that appears in us as a result of a visual contact with a diagram, and visual “intuition of” a mathematical object may appear when we have a tendency to visualize this object while thinking or reasoning with it (this may be the case with objects like a triangle, graph, lattice, as well as number line). Finally, it is stressed that many analyses of the use of diagrams and visualization in mathematics completely dispense with the use of the term “intuition”.
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